The mediating effect of engagement in the relationship between self-efficacy and perceived learning in the online mathematics environment among Chinese students

doi:10.21203/rs.3.rs-4673196/v1

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The mediating effect of engagement in the relationship between self-efficacy and perceived learning in the online mathematics environment among Chinese students

https://doi.org/10.21203/rs.3.rs-4673196/v1

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Perceived learning is considered an indicator of actual learning and is a crucial component of course evaluation. This study explored the mediating effect of learning engagement on the relationship between learning self-efficacy and perceived learning in an online mathematics environment. Using a predictive correlational research methodology, the study examined how the three elements of learning engagement influence the relationship between learning self-efficacy and perceived learning. A randomly selected sample of 605 students enrolled in online mathematics courses in Guangzhou participated in the survey. Structural Equation Modelling (SEM) with AMOS version 24.0 was used to evaluate the hypothesized model. The maximum likelihood estimation results indicated that the measurement model for learning self-efficacy, engagement, and perceived learning had an acceptable fit. The findings demonstrated that learning self-efficacy directly predicts all three sub-constructs of learning engagement in an online mathematics environment. Furthermore, the results revealed a direct relationship between learning self-efficacy and perceived learning, with all three dimensions of learning engagement partially mediating this link. Overall, the intricate interplay between these factors highlights the importance of enhancing student self-efficacy and engagement to foster effective online learning experiences and outcomes.

engagement

mathematics education

perceived learning

self-efficacy

SEM

In light of the advancement of communication technology and the widespread availability of the Internet, online education has become increasingly accessible and has been steadily expanding globally [1]. The COVID-19 pandemic has significantly accelerated the growth of China’s online education market. Since 2017, the number of online users has increased annually, reaching 377 million in 2020, accounting for 40.5% of all users [2]. Currently, China's online education encompasses five main sectors: preschool education, K-12 education, higher education, vocational education, and other types of education [3]. Among these, K-12 education is the largest, with the Smart Education of China platform for K-12 boasting a registered population of 72.51 million and over 700 million cumulative views [4]. However, with the easing of COVID-19 restrictions and the implementation of China's 'Double Reduction' policy and other online education measures, the number of student registrations for K-12 online education has been impacted [3]. Given the cognitive and physical development stages of teenagers, it is crucial to prioritize online education for adolescents. Therefore, it is essential to explore the factors that may influence the best practices for organizing online courses.

Previous research has emphasized the importance of student learning outcomes as validly measured indicators of online education's success [6]. When comparing traditional and online learning, accomplishment is considered crucial. Perceived learning predicts students’ academic grades [7]. Furthermore, Stein and Wheaton [8] contended that perceived learning may predict accomplishment more than course outcomes or final grades. Perceived learning has been considered an indicator of learning and is one of the core elements of course evaluation [9].

Perceived learning provides instructors with valuable insights from the learner's perspective, enhancing the design, delivery, and assessment of online courses, and ultimately improving the online learning experience for students [10]. Additionally, perceived learning serves as a retrospective evaluation of the learning experience [11]. Students who believe they have thoroughly studied the course materials are more likely to actively participate in online sessions [12]. Consequently, student-perceived learning can help quantify a course's success or failure. Understanding the factors influencing perceived learning enables instructors to improve the quality of online courses, including their design, delivery, and assessment, thereby enriching the students' learning experience [13]. Evaluating students' perceptions of their learning is crucial for educators and instructional designers to enhance online course quality and improve the students' learning experience.

Self-efficacy for online learning is a significant factor related to learning outcomes. Increased self-efficacy is essential for fostering technology acceptance, improving learning, and enhancing students' academic performance and perceived learning in online environments [14]. Students often find asynchronous activities (e.g., reading materials, assignments, exercises, and quizzes) challenging to assess, teach, and consult [15]. The difficulties students encounter in problem-solving are often due to the inability to effectively activate existing knowledge rather than a lack of mathematical knowledge. Furthermore, student engagement is seen as a proxy for learning quality due to its contribution to positive learning outcomes, deep learning, critical thinking, retention rates, and student satisfaction [16, 17]. It is crucial for understanding and improving student learning [18, 19]. Previous studies have shown that student engagement in online classes significantly enhances retention rates and reduces feelings of isolation [21, 36]. Online learning engagement, characterized by meaningful interaction and communication, encompasses the time, effort, energy, thought, and feelings that students invest in their learning process, and is considered a valid indicator of the quality of online education [22, 23].

As indicated by the existing literature review, empirical evidence on online self-efficacy and engagement has highlighted various factors influencing students' learning outcomes. However, the specific interplay between learners' perceptions of self-efficacy, learning engagement, and mathematical factors in educational contexts, particularly in online mathematics education, remains underexplored. Therefore, this study aimed to investigate how learning engagement mediates the relationship between self-efficacy and perceived learning in online mathematics. The study addressed the following research questions: a) Does learning self-efficacy predict the sub-constructs of learning engagement (vigor, dedication, absorption)? b) Do the sub-constructs of learning engagement (vigor, dedication, absorption) predict perceived learning? c) Do the sub-constructs of learning engagement (vigor, dedication, absorption) mediate the relationship between learning self-efficacy and perceived learning? By addressing these questions, the study aimed to contribute to a deeper understanding of the mechanisms through which self-efficacy and engagement influence learning outcomes in the online mathematics learning environment.

2.1 Learning self-efficacy

In the expanding realm of online learning, researchers have focused on the potential role of self-efficacy in enhancing students' perceived learning outcomes [10]. Learning self-efficacy, based on the self-efficacy theory [24] and locus of control theory [25], refers to an individual's confidence in successfully tackling specific learning tasks, activities, actions, or challenges [24]. Essentially, if students doubt their ability to succeed, they are less likely to exert the effort required to achieve their goals [10]. Individuals with high self-efficacy tend to view complex tasks as challenges to be overcome, adopting a positive outlook that enhances their competence and increases the likelihood of successful outcomes [26, 27, 28]. When these individuals face failure, they attribute it to insufficient effort or knowledge, which they believe can be improved [24], thereby increasing their satisfaction, reducing stress, and improving overall well-being [26, 29]. Conversely, those with low self-efficacy perceive complex tasks as threats and tend to avoid them [26].

In the context of mathematics, self-efficacy is a significant factor influencing learners' self-concept and academic achievement [30, 31]. Alqurashi [10, 29] identified self-efficacy in online learners as the strongest predictor of perceived learning, aiding their pursuit of learning goals. Students with high self-efficacy are known to demonstrate greater perseverance and resilience when faced with mathematical challenges [30]. Recent studies emphasize the importance of psychological variables, such as self-efficacy, in enhancing learning abilities and improving academic performance and perceived learning in online settings [14, 32]. Yunusa and Umar's review [33] suggests that self-efficacy and academic engagement are key predictors of perceived learning in e-learning environments. However, more research is needed to fully understand the relationship between self-efficacy and perceived learning in online settings [10]. This relationship is complex, influenced by factors such as prior online learning success, technology anxiety, instructor feedback, and class preparation [34]. Research in mathematics learning has highlighted how learners' belief in their abilities impacts their mathematical achievements, particularly in asynchronous online learning environments. Continued exploration of the interactions between self-efficacy and perceived learning outcomes is essential for understanding what promotes successful learning outcomes for secondary students in the digital age.

With advancements in technology and the rise of web and internet technologies, students are increasingly willing to use and interact with technology for communication. This shift has led researchers to investigate context-specific self-efficacy in virtual learning environments, resulting in distinct constructs like computer self-efficacy, internet self-efficacy, and online learning self-efficacy [29]. Recent research has focused on the connection between learning self-efficacy and other constructs, including learning engagement in online contexts [35, 36, 37]. For instance, Wu [37] studied Chinese EFL students' learning self-efficacy, engagement, and social presence in an online environment, finding that online learning self-efficacy predicts engagement and enhances it through learners’ social presence. Derakhshan and Fathi [35] also found that online learning self-efficacy significantly positively impacts engagement among 578 EFL learners. Martin and colleagues [36] discovered that students with high online learning self-efficacy were more engaged in the classroom and that this self-efficacy correlated with increased achievement.

In mathematics learning, only one study has examined the relationship between students’ learning self-efficacy and engagement in an online environment. Spence and Usher [38] compared traditional and online students regarding the impact of computer self-efficacy on courseware engagement, concluding that computer self-efficacy significantly influenced engagement in online environments but not in traditional settings. In a conventional secondary mathematics classroom setting, Ozkal [39] found that students’ mathematics self-efficacy significantly predicted their learning engagement and mathematical performance. Investigating self-efficacy in online education is crucial, as it provides insights into factors influencing learners' engagement and success. As research deepens, understanding the role of online self-efficacy in promoting engagement and achievement in online learning environments will help optimize learners' experiences in online mathematics education.

2.2 Learning engagement

The overarching construct of engagement remains pertinent in both online and traditional classrooms, although its conceptualization has evolved over time. Engagement can be defined as the extent of an individual's productive participation and persistence in various activities [40]. In the educational context, it refers to a positive, fulfilling state of mind marked by vigor, dedication, and absorption, encompassing students' aspirations, a sense of belonging, and productivity [41]. This construct is characterized by three core dimensions: vigor, dedication, and absorption, and is widely recognized as the learners' enthusiasm, motivation, and determination to actively participate and succeed in their own learning [42, 43]. As a key indicator of students' positive psychological engagement in learning, it reflects their positive and healthy mental state. Engagement helps cultivate qualities such as optimism, resilience, a sense of meaning, and creativity, thereby promoting students' development and preparing them for future societal integration [44].

Research on learning inputs has evolved from a uni-dimensional to a multi-dimensional approach, with existing studies on learning inputs broadly categorized into two-dimensional, three-dimensional, and four-dimensional structures [42]. Initially, researchers defined learning engagement as learners actively participating in school-provided activities [45], focusing primarily on the behavioral dimension, which includes positive attitudes and learning behaviors while excluding negative experiences during learning activities. However, this concept has been criticized for its narrow focus on behavioral variables, though it paved the way for further discussions in the educational field [43]. Later, Schaufeli and colleagues [41, 46], from a psychological perspective, described learning engagement as students' involvement in learning tasks and activities akin to "work." In this view, students are engaged in mandatory, structured tasks (e.g., completing assignments, attending class) and activities aimed at specific goals. Consequently, this study defines learning engagement through three dimensions: vigor, dedication, and absorption.

Vigor is characterized by high energy and mental resilience when working on study-related tasks, along with a willingness to exert effort even in the face of difficulties. Dedication involves deep engagement in one's studies, marked by feelings of significance, enthusiasm, inspiration, pride, and challenge. Absorption refers to being fully concentrated and joyfully engaged in learning to the extent that time seems to pass quickly, making it difficult to disengage from studies [40]. Each of these dimensions has unique qualities and significantly influences students’ engagement levels in educational settings [42, 44]. These dimensions align with Fredrick's constructs of behavioral, cognitive, and emotional engagement, illustrating that academic engagement now encompasses individuals' feelings, behaviors, and thought processes [43]. However, engagement in schoolwork and the experience of flow share conceptual similarities [41], indicating that engagement can operate on different timescales.

Research consistently shows that students exhibiting high levels of vigor, dedication, and absorption tend to perform well academically, experience high life satisfaction, and show fewer depressive symptoms [47]. For instance, Tuominen-Soini and Salmela-Aro [48] identified four groups among high school students: dedicated, dedicated-exhausted, cynical, and burned-out. Despite higher stress levels, engaged students were more academically successful and more likely to attend college. The patterns of engagement and burnout remained stable from adolescence to early adulthood. Additionally, a cross-sectional study by Teuber et al. [49] involving 1,527 Chinese high school students and 850 vocational high school students found that the three dimensions of learning engagement (vigor, dedication, and absorption) were inversely correlated with emotional exhaustion and positively associated with self-efficacy, perseverance, teacher-student relationships, and life satisfaction. This study also highlighted the strong psychometric properties of this framework within the Chinese educational context. Although multiple studies have demonstrated the correlation between learning engagement and academic performance, literature examining the relationship between learning engagement and perceived learning is limited, particularly in online learning. Thus, addressing this gap is crucial for enhancing our understanding of online learning dynamics and improving educational methods in the digital age.

2.3 Perceived learning

The purpose of any education, traditional or online, is to learn. The level of learning achieved, which is frequently measured by academic grades or perceived learning, can be used to evaluate the quality of a course. Student learning is an important indication of educational results and is frequently used to assess the quality of courses. Learning has two sub-constructs: actual achievement, which relates to the grades students obtain, and perceived learning, which is based on students' self-reported learning experiences [6]. Perceived learning is the learner’s self-evaluation of whether the course helped achieve its learning goals [50]. According to Rovai [50], student grades are not necessarily a good indicator of what a student has learned because students may come to class with prior knowledge, and grades may also represent class participation, timely submission of work, or attendance. Perceived learning is an important aspect of online education because if students report that their learning is inadequate, the instructor must consider improving the course design to increase learning [51].

Many other aspects of learning need to be considered when assessing what a student has learned [52]. Previous research has demonstrated the validity of self-reports of students' cognitive learning, and evidence from these studies suggests consistency of results over time and across populations [53]. For example, Stein and Wheaton [8] contended that perceived learning may be a greater predictor of achievement than course accomplishments or final grades. Perceived learning has been considered an indicator of learning and is one of the core elements of course evaluation [9].

On the one hand, perceived learning provides instructors with useful insights from the learner's perspective, which improves the quality of online courses in terms of design, delivery, and assessment, eventually increasing students' online learning experiences [10]. On the other hand, perceived learning provides a retrospective evaluation of the learning experience [11]. Students who believe they have mastered course materials are more likely to actively participate in online classes [12]. Therefore, student-perceived learning helps measure the success or failure of any course. Understanding the factors influencing perceived learning can empower instructors to enhance the quality of online courses, encompassing course design, delivery, and assessment, thereby enriching the learning experience for students [13]. Thus, educators and instructional designers must evaluate how students perceive their learning to improve the quality of online courses in terms of course design, delivery, evaluation, etc., as well as improve the student’s learning experience.

2.4 Learning engagement as the mediator of the relationship between self-efficacy and perceived learning in the online mathematics environment

Previous research has consistently demonstrated the linkage between self-efficacy and engagement, self-efficacy and perceived learning, and engagement and perceived learning. Despite the limited number of prior studies in various educational settings, investigating the mediating effect of learning engagement in the relationship between learning self-efficacy and perceived learning in the online learning environment of mathematics is relatively non-existent. As such, this present study is relevant to studies in the subsequent discussion.

Panigrahi et al. [54] found that all dimensions of learning engagement fully explain the positive association between internet self-efficacy and perceived learning effectiveness in online education among Indian postgraduates. In line with the findings, Nia et al. [55] conducted a cross-sectional study to evaluate how student acceptance and satisfaction with online learning and self-efficacy influenced university student participation during the COVID-19 pandemic in nine different countries. Both study models indicated that student engagement as an indicator can modulate the relationship between self-efficacy and achievement in the online learning environment. According to Bandura's self-efficacy theory, students' motivation, learning state, and learning outcomes are all affected by their subjective perception of their ability to perform and succeed [56]. Furthermore, learning self-efficacy is a proximate element regulating the level of involvement in learning and can accurately predict engagement in learning [57].

As a result, it is reasonable to conclude that online learners' confidence in their abilities to manage and conduct internet-related tasks improves their perceived learning outcomes. This enhancement is mediated through various dimensions of learning engagement, such as vigor, which is characterized by high levels of energy and mental resilience while learning; dedication, which involves a sense of significance, enthusiasm, and pride in one's learning tasks; and absorption, where students are entirely concentrated and happily engrossed in their learning activities. In conclusion, understanding the interplay between self-efficacy, engagement, and perceived learning is crucial for optimizing online learning environments, especially in subjects like mathematics, where engagement can be particularly challenging. Future research should continue to explore these relationships in diverse educational settings and consider interventions that can boost self-efficacy and engagement to improve learning outcomes.

Based on the above empirical research, this study considers the possible mediation roles of online learning engagement to explore the relationship between learning self-efficacy and perceived learning in an online mathematics environment. The following conceptual model is shown in Fig. 1. Only some prior studies have examined the complex relationships between learning self-efficacy, learning engagement, and perceived learning in online learning environments. The current study has the following hypothesis:

Ha1: Learning self-efficacy is positively related to vigor

Ha2: Learning self-efficacy is positively related to dedication

Ha3: Learning self-efficacy is positively related to absorption

Ha4: Learning self-efficacy is positively related to perceived learning

Ha5: Vigor is positively related to perceived learning

Ha6: Dedication is positively related to perceived learning.

Ha7: Absorption is positively related to perceived learning

Ha8: Vigor mediates the relationship between learning self-efficacy and perceived learning.

Ha9: Dedication mediates the relationship between learning self-efficacy and perceived learning.

Ha10: Absorption mediates the relationship between learning self-efficacy and perceived learning

3.1 Participants and design

This study used the predictive correlational research design, which explores the mediating effect of all three dimensions of learning engagement in the relationship between learning self-efficacy and perceived learning using structural equation modeling (SEM). Predictive correlational research design is essential for comprehending and forecasting the relationships between variables across different fields. Researchers can make well-informed predictions about outcomes based on these identified associations by employing statistical analyses to assess the connections between variables. The current study sample consisted of 9 grader secondary school students studying the online mathematics program in Guangdong Province, China, with similar modeling experiences. This study conducted an online survey in the spring semester of 2024.

605 students from a specific region in Guangzhou were chosen randomly to take part in an online mathematics course survey. Prior to completing the questionnaire, students received information about the study's objectives, and their participation was voluntary. The survey included questions about demographic details and assessments on interaction, self-efficacy in online learning, academic emotions, and learning engagement. All questionnaires were presented in Chinese.

3.2 Instruments

Learning self-efficacy scale

The instrument utilized in this research measures student online learning self-efficacy. The instrument was adapted from Li et al. [58], providing four Likert scales for each question. The instrument was selected because it has been validated by Chinese scholars, including Li et al. [58], in the educational field within the Chinese educational environment. However, the research will use five Likert scales since research showed that past researchers mainly used five Likert scales to measure self-efficacy among respondents [59]. Some adaptations have been made from the sources. The instrument is a unidimensional scale comprising 14 items to assess learners' perception of their learning self-efficacy toward their online mathematics learning. An example of the question was, “I have clear learning goals in the online mathematics course.” Respondents must select their answer for every question on a 5-point Likert scale from 1 (strongly disagree) to 5 (strongly agree).

Learning engagement scale

The instrument used in this research is the Utrecht Work Engagement Scale developed by Schaufeli et al. [46]. This questionnaire was used because the item is simple, easy to administer, and suitable for measuring online learning engagement. This instrument consisted of 18 items to assess learners' learning engagement during online mathematics learning, among which six items were used to measure vigor, six were used to measure dedication, and six were used to measure absorption. Examples of the three subscales were: “When I get up in the morning, I feel like going to the online mathematics class,” “To me, online mathematics learning is challenging,” and “When I am online mathematics learning, I forget everything else around me.” The score for the negative item is reversed during data analysis. This questionnaire used the Likert scale to measure the level of learning engagement in the online learning environment. There are five scale choices from 1 to 5.

Perceived learning scale

The perceived learning questionnaire has been used to measure the level of student-perceived learning in the online education setting. The instrument was developed by Gray and DiLoreto [60]. This questionnaire was used because it is the most used to measure student-perceived learning within the online learning environment. This section consists of 6 questions regarding student online learning perceived learning. A sample item was “I am pleased with what I learned in the online mathematics course.” The score for the negative item is reversed during data analysis. The items will be graded on a five-point Likert scale, with one denoting "strongly disagree," 2 denoting "disagree," 3 denoting "neutral," 4 denoting "agree," and five denoting "strongly agree.".

3.3 Data analysis

In the initial analysis, we used SPSS 22.0 to perform descriptive statistics for all sub-constructs, accounting for missing data and outliers (using boxplots), and calculated means, standard deviations, skewness, and kurtosis. Pearson correlations were used to determine the relationships between latent variables and check for multicollinearity, ensuring that the relationships between latent variables were below 0.900 to avoid multicollinearity [61]. For assessing univariate normality, we used skewness values within ± 2.0 [62] and kurtosis values within ± 8.0 [61]. Following this, we employed Structural Equation Modeling (SEM) using AMOS version 24.0 to evaluate the hypothesized model. Initially, a measurement model (Confirmatory Factor Analysis—CFA) was calculated for each variable to confirm the dimensional structures of the instruments for the sample. We sequentially assessed the vigor, dedication, and absorption models for learning engagement, followed by evaluating two unidimensional constructs: learning self-efficacy and perceived learning.

We then established the hypothetical model to test the mediating effect of the three sub-constructs of learning engagement (vigor, dedication, and absorption) between learning self-efficacy and perceived learning. Model fit was assessed using various indices: standardized root mean residual (SRMR) (< 0.080), chi-square values (P > 0.05), comparative fit index (CFI) (> 0.900), Tucker-Lewis index (TLI) (> 0.900), root mean square error of approximation (RMSEA) (< 0.080), and the goodness-of-fit index (GFI) (> 0.900) [63]. According to Hu and Bentler [64], a model is considered acceptable if χ2/df ≤ 5, RMSEA and SRMR < 0.08, and CFI and TLI > 0.9. A model is considered a good fit if RMSEA < 0.05 and CFI and TLI > 0.95. Additionally, the Bootstrap regression path analysis method was used to test the significance of the model’s mediating effects.

4.1 Descriptive results

The descriptive statistics, including the mean, standard deviation, skewness, and kurtosis of the primary constructs, namely learning self-efficacy and perceived learning and sub-construct of learning engagement (vigor, dedication, and absorption) in this study, are presented in Table 1.

As indicated in Table 1, the mean scores for the learning self-efficacy and perceived learning constructs were moderate (M = 3.68, M = 3.52, respectively). Learning engagement, vigor, dedication, and absorption were also moderate (M = 3.61, M = 3.51, M = 3.62, respectively).

Table 1

Descriptive output of each construct
Construct	Sub-construct	Mean	Std.	Skewness	Kurtosis
Learning self-efficacy	/	3.68	1.01	-0.96	-0.85
Learning engagement	Vigor	3.61	1.02	-0.71	-0.91
	Dedication	3.51	1.01	-0.41	-1.27
	Absorption	3.62	1.00	-0.73	-0.93
Perceived learning	/	3.52	1.14	-0.68	-1.10

Subsequently, Table 2 shows the correlation matrix for the sub-construct of learning engagement (vigor, dedication and absorption). As indicated in Table 2, statistically significant correlations were found between absorption and dedication (\(\:\gamma\:=0.65)\), absorption and vigor (\(\:\gamma\:=0.65)\), and dedication and vigor (\(\:\gamma\:=0.59)\). The research findings indicate that the learning engagement sub-constructs are free from multicollinearity issues, thus fulfilling the discriminant validity for learning engagement variables.

Table 2

Multicollinearity output for learning engagement
Sub-constructs of learning engagement	1	2	3
1.Absorption	1.00
2.Dedication	0.65	1.00
3.Vigor	0.65	0.59	1.00

4.2 Measurement models

The measurement model was employed to ensure that the observed variables accurately represented the latent variables before assessing the hypothetical structural model. Confirmatory Factor Analysis (CFA) was utilized to evaluate the adequacy of the latent variables, including learning self-efficacy (14 indicators), perceived learning (6 indicators), and learning engagement comprising vigor (6 indicators), dedication (6 indicators), and absorption (6 indicators). The outputs from the maximum likelihood estimation revealed that the measurement model for learning self-efficacy indicated an acceptable fit: χ2 = 83.087, χ2/df = 1.079, RMSEA = 0.011, CFI = 0.980, GFI = 0.981, TLI = 0.989 (Table 3). The measurement model for learning engagement also indicated an acceptable fit: χ2 = 116.927, χ2/df = 1.008, RMSEA = 0.04, CFI = 0.981, GFI = 0.977, TLI = 0.980. Furthermore, the measurement model for perceived learning demonstrated a good fit to the data: χ2 = 9.445, χ2/df = 1.049, RMSEA = 0.009, SRMR = 0.0087, CFI = 0.987, GFI = 0.995, TLI = 0.950. Despite the significance of the chi-square result, the χ2/df, RMSEA, SRMR, CFI, GFI, and TLI values recommended that the a priori model had an adequate factor structure.

Table 3

Examination of the measurement model
Goodness-of-fit	Measurement standard	Results
		Learning self-efficacy	Perceived learning
χ2	P > 0.05	83.087	9.445
χ2/df	< 5.00	1.079	1.049
RMSEA	< 0.080	0.011	0.009
CFI	> 0.950	0.980	0.987
GFI	> 0.900	0.981	0.995
TLI	> 0.950	0.989	0.950

All types of assessments indicate that the model is suitable for the learning engagement construct, as the fit indices for χ², χ²/df, CFI, and RMSEA show acceptable values. However, one item (Q26) of the dedication sub-construct exhibits low factor loadings (0.56). Therefore, items with low factor loadings were excluded to improve the model fit in this study. Referring to Table 5, there is one item with low factor loadings: item Q26 (sub-construct dedication) with a factor loading of 0.56. Consequently, Model 2 was tested by removing item Q26. After conducting the CFA test estimation again by removing item Q26, the result indicates that the goodness-of-fit also meets the criteria (Table 4). Model 1 showed the following fit indices: χ2 = 406.083, χ2/df = 3.076, RMSEA = 0.059, CFI = 0.957, GFI = 0.936, TLI = 0.950. In comparison, Model 2, after removing item Q26, showed improved fit indices: χ² = 116.927, χ²/df = 1.008, RMSEA = 0.04, CFI = 0.981, GFI = 0.977, and TLI = 0.980.

Table 4

Examination of the measurement model for learning engagement
Goodness-of-fit	Measurement standard	Results
		Model 1	Model 2
χ2	P > 0.05	406.083	116.927
χ2/df	< 5.00	3.076	1.008
RMSEA	< 0.080	0.059	0.004
CFI	> 0.950	0.957	0.981
GFI	> 0.900	0.936	0.977
TLI	> 0.950	0.950	0.980

In Table 4, the factor loadings and coefficients of SEM regression are presented. All factor loadings for learning self-efficacy ranged from 0.770 to 0.810, for perceived learning from 0.810 to 0.860, and for the sub-constructs of learning engagement (vigor: 0.740–0.790, dedication: 0.760–0.820, absorption: 0.760–0.800) were found to be statistically significant (P < 0.001). Each item within these sub-constructs demonstrated strong factor loadings, confirming the consistency among items for each respective sub-construct. The standardized estimates for factor loadings exceeded 0.50 for all items, meeting the recommended criteria [65].

Table 5

Factor loadings of variables
Construct	Sub-construct	Item	Factor loading	P
Learning self-efficacy	/	Q1	0.793	***
		Q2	0.788	***
		Q3	0.783	***
		Q4	0.787	***
		Q5	0.767	***
		Q6	0.769	***
		Q7	0.791	***
		Q8	0.778	***
		Q9	0.788	***
		Q10	0.783	***
		Q11	0.779	***
		Q12	0.812	***
		Q13	0.784	***
		Q14	0.755	***
Learning engagement	Vigor	Q15	0.736	***
		Q16	0.749	***
		Q17	0.786	***
		Q18	0.795	***
		Q19	0.785	***
		Q20	0.764	***
	Dedication	Q21	0.766	***
		Q22	0.773	***
		Q23	0.76	***
		Q24	0.816	***
		Q25	0.776	***
		Q26	0.563	***
	Absorption	Q27	0.798	***
		Q28	0.777	***
		Q29	0.756	***
		Q30	0.757	***
		Q31	0.763	***
		Q32	0.794	***
Perceive learning	/	Q33	0.829	***
		Q34	0.806	***
		Q35	0.813	***
		Q36	0.862	***
		Q37	0.819	***
		Q38	0.814	***
***Significant.

4.3 Testing the hypothesized models

We established a direct effect model to explore the predictive effects of learning self-efficacy on perceived learning (see Fig. 2). Similar to examining the measurement model, various goodness-of-fit values were also considered for each measurement to test the structural model: χ2/df < 5.00, RMSEA < 0.080, SRMR < 0.080, CFI > 0.950, GFI > 0.900, TLI > 0.950. The results of SEM indicated a highly satisfactory fit to data, χ2 = 159.400, χ2/df = 0.943, RMSEA = 0.000, SRMR = 0.0159, CFI = 0.989, GFI = 0.975, TLI = 0.998 (see Fig. 2). The results showed that learning self-efficacy [β = 0.580, P < 0.01] could significantly predict perceived learning.

Using the direct effect model as a basis, we conducted a multiple mediating effect model incorporating the three sub-constructs of learning engagement (vigor, dedication, and absorption) as mediators to explore the relationship between learning self-efficacy and perceived learning (see Fig. 3). The fit indices for the multiple indirect effects model were satisfactory: χ2 = 1028.814, χ2/df = 1.654, RMSEA = 0.033, CFI = 0.973, GFI = 0.916, TLI = 0.971 (see Fig. 3). The results indicated that learning self-efficacy [β = 0.360, P < 0.01] predicted vigor, which in turn predicted perceived learning [β = 0.150, P < 0.01]; secondly, learning self-efficacy [β = 0.470, P < 0.01] predicted dedication, which also predicted perceived learning [β = 0.210, P < 0.01]. Thirdly, learning self-efficacy [β = 0.150, P < 0.01] predicted absorption, with the indirect path coefficient from absorption to perceived learning being significant [β = 0.090, P = 0.027 < 0.05].

This study utilized Baron and Kenny's [66] method to investigate whether all three constructs of learning engagement (vigor, dedication, and absorption) mediated the relationship between learning self-efficacy and perceived learning. Based on the bias-corrected bootstrapping test results (Table 6), the indirect effects of learning self-efficacy on perceived learning through vigor (indirect effect = 0.063, 95% CI = [0.029, 0.113]), dedication (indirect effect = 0.114, 95% CI = [0.063, 0.182]), and absorption (indirect effect = 0.044, 95% CI = [0.002, 0.095]) were significant. The results indicated that all three constructs of learning engagement (vigor, dedication, and absorption) mediated the relationship between learning self-efficacy and perceived learning.

Table 6

Bias-corrected bootstrap test
Model pathways	Estimate	95% CI		P
		Lower	Upper
LSE—>vigor—>perceived learning	0.064	0.029	0.113	0.001
LSE—>dedication—>perceived learning	0.114	0.063	0.182	0.000
LSE—>absorption—>perceived learning	0.044	0.002	0.095	0.039
Note: LSE = learning self-efficacy

Table 7

Distinguishing direct and indirect effects of the mediating model.
Mediator	Direct effect	Indirect effect	Decision
Vigor	0.36 (p < 0.05)	0.054 (p < 0.05)	Partial Mediation
Dedication	0.47 (p < 0.05)	0.0987 (p < 0.05)	Partial Mediation
Absorption	0.44 (p < 0.05)	0.0396 (p < 0.05)	Partial Mediation

Based on Table 7 and the multiple mediating effect model (Fig. 3), the study indicates that when both the direct relationship between the independent variable (learning self-efficacy) and the dependent variable (perceived learning) and the indirect relationships through vigor, dedication, and absorption are significant, partial mediation occurs [66]. In this study, the direct effect of learning self-efficacy on perceived learning was significant, as were the indirect effects through vigor, dedication, and absorption. Therefore, vigor, dedication, and absorption collectively partially mediate the relationship between learning self-efficacy and perceived learning.

Building on theoretical frameworks and previous empirical research, this study investigated the mediation role of learning engagement in the relationship between learning self-efficacy and perceived learning within the context of online mathematics education. Specifically, the study explored whether the sub-constructs of learning engagement (vigor, dedication, and absorption) mediate this relationship. The results underscored the significance of learning engagement in elucidating the association between self-efficacy and perceived learning. Furthermore, the study identified distinct predictive and mediating mechanisms among the three types of engagement in influencing perceived learning outcomes. These findings contribute to existing theories and offer practical insights for enhancing online educational practices.

Firstly, the results of our study indicated that learning self-efficacy directly predicts all three sub-constructs of learning engagement in the online mathematics environment which fully supports Hypothesis a1 to a3. The finding is in line with previous research [37, 67, 68], where their result demonstrated that learning self-efficacy has a direct significant positive contribution to learning engagement in the online learning environment. Specifically, the result also revealed that learning self-efficacy directly predicts all three sub-construct of learning engagement (vigor, dedication and absorption). This finding aligns with self-efficacy theory [24], suggesting that confident individuals are more likely to approach difficult tasks with more effort and determination. Student in the online mathematics environment might be more satisfied with the online learning environment regarding their learning process and feel more confident in their mathematics learning ultimately improving their learning engagement for learning mathematics. Therefore, students should be provided with appropriate resources and training to enhance their online learning self-efficacy beliefs and generate online learning engagement regarding vigor, dedication and absorption. This perspective has been proved by Wu [37], who found that Chinese online learners found the online learning environment to be effective in motivating them to learn and were satisfied with and engaged in the online learning process.

Secondly, our study confirmed a direct relationship between learning self-efficacy and perceived learning in the online mathematics environment, supporting Hypothesis a4. This finding aligns with previous studies by Navarro et al. [14] and Alqurashi [10, 69], which suggest that online learners' perceptions of their own learning efficacy significantly influence their capacity for self-directed learning. Online learners who possess high levels of learning confidence are more likely to perceive their learning experiences positively. They demonstrate confidence in their ability to achieve good grades, handle challenging topics, manage their study schedules effectively, plan and assess assignments using rubrics, and meet course expectations [10]. It can be inferred that the increase in self-efficacy, often derived from prior successful experiences, significantly enhances their perception of learning outcomes. Besides that, when faced with difficulties, they are more likely to remain calm and believe in their ability to find solutions, exhibiting greater perseverance and resilience when encountering challenges. Therefore, students with high levels of self-efficacy for learning are more likely to perceive more excellent learning outcomes. This corroborates the review made by Alqurashi [29], who argued that online learners with high self-efficacy are more likely to believe in their abilities, leading to greater motivation to engage in the online learning process. Confidence in the online environment empowers learners learning outcomes, thus enhancing their perceived learning. Furthermore, our findings align with those of Prabhu M et al.’s findings [32], which also reported a positive predictive relationship between online self-efficacy and perceived learning.

Thirdly, our finding revealed that all three dimensions of learning engagement significantly predict learners’ online perceived learning outcomes, supporting Hypothesis a5 to a7 in this study. To our knowledge, no research is specific on the relationship between learning engagement and perceived learning in the context of online learning. However, these findings support prior research on the importance of learning engagement, including vigor, dedication, and absorption [47–49]. For instance, research by Teuber et al. [49] indicated that students with high levels of vigor, dedication, and absorption are associated with a solid ability to persevere, overcome challenges, and maintain high life satisfaction in their studies. Therefore, in the online learning environment, students with high vigor typically exhibit positive emotions and attitudes, making them more optimistic and confident when facing learning tasks. Additionally, students with high dedication have clear direction and purpose in their learning activities, allowing them to focus and effectively utilize learning resources and strategies, enhancing their perception of learning outcomes. Lastly, when students fully absorb their learning tasks, they are more likely to engage in deep information processing and critical thinking. Previous research supports this statement, which argues that fulfilling basic psychological needs, a major driver of engagement, may occur outside the work context [40, 41].

Finally, our study confirmed hypotheses a8 to a10, indicating that all three dimensions of learning engagement—vigor, dedication, and absorption—partially mediate the relationship between learning self-efficacy and perceived learning in the online mathematics environment. This finding is consistent with prior research, particularly the work of Panigrahi et al. [54], which similarly demonstrated that all dimensions of learning engagement fully mediate the positive relationship between internet self-efficacy and perceived learning effectiveness among Indian postgraduate students. Bandura [70] suggests that self-efficacy serves as a psychological state influencing academic outcomes indirectly rather than directly. In essence, students with high vigor remain positive and energized when faced with learning tasks, leading to better engagement in the learning process [41]. Similarly, they are more likely to demonstrate a sense of significance, enthusiasm, inspiration, pride, and readiness to embrace the challenges of online learning, which may lead to more significant effort and engagement in their online learning activities. Students with high self-efficacy, supported by their vigor, dedication, and absorption, can better cope with the various pressures and challenges of online learning. This ability to cope helps them maintain a positive learning experience, enhancing their learning outcomes.

Moreover, self-efficacy can be strengthened or weakened when interacting with others in learning activities. The learning self-efficacy of online learners is correlated with their state of study concerning assigned tasks and activities. In other words, students possess a stronger self-efficacy of being able to fully be absorbed in accomplishing the given tasks related to mathematics learning, which is characterized by focused attention, a clear mind, mind and body unison, effortless concentration, complete control, loss of self-consciousness, distortion of time, and intrinsic enjoyment. At the same time, those who are low self-efficacious may experience negative affective states such as stress, anxiety, and depression that disengage them in the online mathematics learning environment. In other words, students with a stronger self-efficacy are fully absorbed in accomplishing the given tasks related to mathematics learning. Focused attention, a clear mind, mind and body unity, effortless concentration, complete control, loss of self-consciousness, distortion of time, and intrinsic enjoyment characterize this absorption [71]. In other words, students with stronger self-efficacy can fully engage in completing tasks related to mathematics learning, characterized by these positive states. Conversely, those with lower self-efficacy may experience negative affective states such as stress, anxiety, and depression, which disengage them from the online mathematics learning environment.

This study underscores the critical role of learning engagement as a mediating factor in the relationship between learning self-efficacy and perceived learning in an online mathematics environment. The findings affirm that students with higher self-efficacy are more likely to engage vigorously, dedicatedly, and absorbingly in their learning tasks, enhancing their perceived learning outcomes. Specifically, our results indicate that learning self-efficacy directly influences all three sub-constructs of learning engagement—vigor, dedication, and absorption—each of which partially mediates the relationship between self-efficacy and perceived learning. This aligns with the self-efficacy theory, which posits that individuals confident in their abilities are better equipped to tackle challenging tasks with more significant effort and persistence. Furthermore, the study highlights the importance of fostering a supportive online learning environment that enhances students' self-efficacy. Providing appropriate resources and training can help students feel more confident in their online learning capabilities, ultimately improving their engagement and learning outcomes. The empirical evidence from this research supports previous theories and offers practical insights for educators and policymakers aiming to improve online education quality. By understanding and leveraging the dynamics between self-efficacy, engagement, and perceived learning, stakeholders can better support students in achieving optimal educational outcomes in the digital age. The intricate interplay between these factors demonstrates that enhancing student self-efficacy and engagement is paramount for fostering compelling online learning experiences and outcomes.

Acknowledging limitations is crucial in research, and our study is no exception. Firstly, while all hypotheses were supported by the findings, one item (Q26) within the sub-construct of dedication exhibited a relatively low loading factor. This could potentially be attributed to the cognitive development stage of secondary school students. At this stage, students are still developing their cognitive abilities and self-regulation skills, which may affect their understanding of learning purposes and long-term goals. Future research should consider these developmental factors when designing and interpreting studies involving secondary school students in educational contexts. Compared to more concrete and immediate motivations (such as test scores or teacher praise), the concept of learning being "full of purpose" may seem more abstract and complex. Further research is needed to make the question more specific, which makes the concept of "full of purpose" more concrete by adding items such as "I believe learning math helps me solve real-world problems" or "I feel that online math learning enhances my logical thinking skills." Moreover, given the disparity in cognitive levels, future studies may need to expand the sample population to include adult students. Secondly, it is essential to note that this study was surveyed in May 2024 to investigate the academic impact of online learning as of December 2023. However, the online mathematics courses the respondents took were asynchronous, meaning that the online learning occurred outside their regular face-to-face school classes. This suggests that their in-school mathematics learning behaviors influenced the study results. Therefore, future research in foundational online education should take measures to eliminate this potential confounding factor and strive to maintain consistency between online learning and learning assessments.

Thirdly, while our study identified correlations among variables, it's important to note that correlational studies cannot establish causality. Future research should consider employing experimental designs or other methods that allow for the investigation of causal relationships among variables. Experimental designs could involve interventions or manipulations of the independent variable to directly observe its effects on the dependent variable. These approaches would provide clearer insights into how various factors influence the outcomes studied. Additionally, a potential limitation of our study is its reliance on self-reported measures, which may introduce bias or error. Future research could enhance validity by incorporating objective measurements or using multiple data sources. Objective measures might include direct observation or physiological assessments, which can offer more accurate and reliable data. Furthermore, integrating multiple data sources can provide a more comprehensive understanding of the phenomenon under study, as different sources may capture different aspects of the constructs being measured. By employing these methodological improvements, researchers can strengthen the validity and reliability of their findings, thereby advancing our understanding of the relationships between variables in educational contexts.

Funding acknowledgment

This work did not receive funding from specific grants from official funding agencies, private entities, or non-profit organizations.

Conflict of interest

The author has affirmed that no conflicts of interest are related to the topic discussed in this paper.

Ethics approval and consent to participate

This study was approved by the school administration and the ethics committee of Universiti Putra Malaysia (JKEUPM) ref no. “UPM.TNCPI.800-2/1/7”. Written informed consent to participate in this study was provided by the participants' legal guardian/next of kin.

Data availability

The datasets are available upon reasonable request from the corresponding author.

Author contribution

Zhuofan Huang: Conceptualization, Formal analysis, Data collection, Writing – original draft. Riyan Hidayat: Supervision, Writing – review & editing. Ahmad Fauzi Mohd Ayub: Supervision, Writing – review & editing.

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The mediating effect of engagement in the relationship between self-efficacy and perceived learning in the online mathematics environment among Chinese students

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Abstract

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1 Introduction

2 Literature review

2.1 Learning self-efficacy

2.2 Learning engagement

2.3 Perceived learning

3 Methodology

3.1 Participants and design

3.2 Instruments

3.3 Data analysis

4 Results

4.1 Descriptive results

4.2 Measurement models

4.3 Testing the hypothesized models

5 Discussion

6 Conclusion

7 Limitations and suggestions

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References

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